Salinity gradient or nonconvecting solar ponds are patterned after natural, meromictic lakes (Tabor, and Weinberger, 1981). As depth increases in these lakes, the salinity increases to such an extent that the density increases even though the temperature simultaneously increases. The absorption of sunlight in the semi-transparent water causes the temperature increase. This density pattern consequently suppresses cooling by natural convection.
Typically ponds develop four distinct zones. At the surface is a homogenized zone called the upper convective zone (UCZ). This zone is stirred by the wind and evaporation, and is usually 0.2-0.4 m thick. Since it absorbs sunlight but does not help suppress convection, it is desirable to keep the UCZ as thin as possible. In very large ponds, this is often achieved by reducing the fetch over which the wind can build waves by floating a grid of netting on the pond's surface. There are, however, other factors, such as evaporation, that contribute to UCZ development and therefore UCZ control is not fully understood. New methods of UCZ control are likely in the future.
Beneath the UCZ is the nonconvecting zone (NCZ) which is usually 0.9-1.3 m thick. It is in this stratified zone that the salinity, density, and consequently temperature increase with depth. Typically this NCZ temperature increase is 30.degree.-70.degree. C. Salt slowly diffuses through the NCZ, but this process is remarkably slow. Solar ponds have been left for a whole year and remained functional. In actively ponds, salt diffusion is neutralized by adding some concentrated brine at the bottom of the NCZ while washing away the excess salt reaching the UCZ. Salt in this wash water is usually reconcentrated and recycled. An intriguing but untested alternative strategy for maintaining the salt gradient is the "falling pond" (Shachar, U.S. Pat. No. 3,372,691). In this fresh water would be slowly added to the surface of the pond. Simultaneously water vapor would be flashed out of warm brine extracted from below the NCZ. Consequently the NCZ would "fall". The rate of "fall" would be set to precisely counteract the upward diffusion of salt.
The stratified NCZ allows the underlying storage zone (SZ) to maintain a distinctly elevated temperature. This SZ has a high salinity (15% to saturated) and temperature (50.degree.-90.degree. C.), and is intentionally homogenized in salinity and temperature primarily by stirring associated with the process of heat withdrawl. This process involves gently "decanting" SZ brine, removing some heat, and then returning this brine to the SZ usually on the opposite side of the pond. Diffusers must be designed and positioned so that the kinetic energy in the extractions and return flows stirs the SZ but does not erode the NCZ. Nielsen (1980) has suggested positioning a plastic partition between the NCZ and the SZ to help control this erosion and seasonal migrations of this zone boundary. The SZ's thickness is matched to the thermal storage needed in a specific application, and is usually between 1.0 and 4.0 m.
Beneath the SZ is the groundzone (GZ). This zone is important in accurate studies of heat losses from a pond because ground water flows can remove a great deal of heat, and because the conductivity of soil, although highly variable, averages twice that of brine.
Solar ponds have been envisioned primarily as an energy source. The heated brine produced by ponds could be use to drive rankine cycle equipment for power generation, used in desalinization, or used directly in a variety of proesss, water, or space heating applications. The economics of ponds producing energy are coupled to the efficiency. Obviously for high efficiency heat losses must be minimized. Moreover water clarity greatly influences both the efficiency and temperature of heat extraction.
For perspective, the table below refers to Rabi-Nielsen's (1975) and Tybout's (1967) water clarity equations. These empirical equations are used in solar pond analyses, and bracket the water clarity achieved in existing solar ponds of conventional design. Rabi-Nielsen represents clearer water than Tybout. Assuming 7.0% heat withdrawal, small edge heat losses due to a large pond area, and typical insolation, a solar pond should average the temperature elevations shown in the first column.
______________________________________ % HEAT WITHDRAWAL 7.0% 17.0% ______________________________________ (1) Rabl-Nielsen 95.degree. C. 63.degree. C. (2) Tybout 56 29 ______________________________________
For Rabi-Nielsen's water clarity these temperature elevations may seem large, however one experimental solar pond has actually boiled under the summer sun (Weeks and Bryant, 1981). Alternatively, if 17.0% of the incident solar energy is withdrawn, the second column gives the resulting average temperature elevations. By comparing both columns, notice that increasing heat withdrawal diminishes the temperature elevation, and increasing clarity can increase either efficiency or the extractions temperature.
The expected temperature elevation must be considered when the salinity stratification is designed. For static stability, each stratum between the SZ and the UCZ must always stay denser than the overlying stratum. Moreover a complex effect named the double diffusive phenomena imposes a stricter "dynamic" stability requirement. For "dynamic" stability the density gradient with respect to salinity must increase 14% faster than statics requires (Tabor and Weinberger, 1981). The dynamic stability criterion may be even stricter over 3-6 month periods (Wittenberg, 1982). Israeli researchers use a still stricter criteria (change in salinity across the NCZ in Kg/m.sup.3)/(change in .degree.C. across the NCZ) .gtoreq. 2.0. These criteria could be conservative if applied to temperatures between 0.degree.-30.degree. C. since density is less sensitive to temperature in this range.
Another aspect of stability involves the most intense period of insolation, the summer solstice. The salinity gradient must be constructed so that during this solstice the local temperature gradient never becomes destabilizing in the most intensely absorbing stratum, at the top of the NCZ. During the rest of the year, obviously, such a salinity gradient would be more stable than is required. The UCZ thickness and water clarity influence the peak absorption intensity and therefore this aspect of stability. This problem can be controlled simply by using an UCZ with a typical thickness.
The following density data adopted from the international Critical Tables (1980) provides perspective on static stability.
______________________________________ T (.degree.C.) NaCl % density (*10.sup.-3) ______________________________________ 100.degree. C. 7.0% 1,0064 kg/m.sup.3 50.degree. C. 2.0% 1.00161 30 1.0% 1.00261 25 3.5% 1.02176 20 0.5% 1.01786 10 0.5% 1.00340 10 0.0% 0.99972 4 0.0% 1.00000 0 0.0% 0.99987 ______________________________________
Notice a 7.0% increase in salinity will offset the thermal expansion between 0.degree. and 100.degree. C. In the 0.degree.-30.degree. C. range, moreover, the effect of thermal expansion on density is milder, and can be offset by only a 1% change in salinity. Consequently, freezing fresh water would easily float on 25.degree. C. seawater (3.5% salinity). For a temperature elevation from 10.degree. C. to 25.degree. C. a salinity increase from 0.5% to 3.5% will provide dynamic stability even using the stricter Israeli criteria since (30 Kg/m.sup.3)/15.degree. C. .gtoreq. 2.0. The inventor has experimentally demonstrated a solar pond using fresh water overlying seawater and 5.degree.-20.degree. C. elevations over a three month period. Also notice that the temperature change between 0.degree. C and 10.degree. C. has a very minor effect on density; a pond will be virtually as stable in a 0.degree. C. environment as in a 10.degree. C. environment.
In addition, two major destabilizing forces, wind and large temperature differences, will often not coincide. The difference between a SZ's temperature and ambient will usually peak at dawn due to night cooling. Simultaneously the wind will usually be slight at dawn.